Question

combining like terms with negative coefficients & distribution
simplify to create an equivalent expression.

-3(2 + 4k) + 7(2k - 1)

choose 1 answer

a 2k - 13

b 8k - 13

c 2k + 13

d 2k - 7

Explanation:

Step1: Apply the distributive property

First, we distribute -3 into (2 + 4k) and 7 into (2k - 1).
For -3(2 + 4k), we multiply -3 by 2 and -3 by 4k:
$-3\times2 + (-3)\times4k = -6 - 12k$
For 7(2k - 1), we multiply 7 by 2k and 7 by -1:
$7\times2k + 7\times(-1) = 14k - 7$
So the expression becomes:
$-6 - 12k + 14k - 7$

Step2: Combine like terms

Now we combine the like terms. The like terms for the k terms are -12k and 14k, and the constant terms are -6 and -7.
Combining the k terms:
$-12k + 14k = 2k$
Combining the constant terms:
$-6 - 7 = -13$
Putting it together, we get:
$2k - 13$

Answer:

A. $2k - 13$